Screening of electrode materials for ammonium ion batteries by high throughput calculation

Ammonium-ion batteries (AIBs) have attracted intense interest lately as promising energy storage systems due to their light weight, safe, inexpensive, and widely available advantages. It is of great significance to find a fast ammonium ion conductor for the electrode of AIBs that directly affects the electrochemical performance of the battery. Using high-throughput bond-valence calculation, we screened the electrode materials of AIBs with a low diffusion barrier from more than 8000 compounds in the ICSD database. Twenty-seven candidate materials were finally identified by the bond-valence sum method and density functional theory. Their electrochemical properties were further analyzed. Our results, which give the relationship between the structure and electrochemical properties of various important electrode materials which are suitable for AIBs development, may pave the way for next-generation energy storage systems.


Introduction
With the worldwide emphasis on renewable energy sources such as solar and wind, battery energy storage has become an essential solution for grid stability and reliability. Traditional metal ion batteries (Li + , 1 Na + , 2 K + , 3 etc.) are relatively expensive in terms of abundance in Earth's crust and mining cost. Emerging non-metallic batteries (proton, 4 NH 4 + , 5 Cl − , 6 etc.) have developed rapidly in recent years. Their cost, capacity, operating voltage, rate performance, and cycle stability are better than metal batteries. Among them, ammonium-ion batteries (AIBs) are promising candidates for large-scale energy storage systems. Compared with metal batteries, ammonium ions have the merit of low molar mass (18 g mol −1 ), rich reserves and being renewable (only containing N and H essential elements), and having smaller hydrated ion sizes. 7,8 Compared with acidic electrolytes, electrolytes containing NH 4 + show weak acidity and are less corrosive, will not lead to the dissolution of electrode materials and have higher HER (hydrogen evolution reaction) overpotential than electrolytes containing H + . 9,10 The progress of ammonium-ion batteries (AIBs) 5,9,[11][12][13][14][15] is still in its infancy. Ji's team systematically studied the insertion of NH 4 + into layered V 2 O 5 . It was found that ammonium-ion forms strong hydrogen bonds with layered V 2 O 5 , and the diffusion mode of NH 4 + is similar to monkey swing. 11 Wang also developed NH 4 + storage based on supercapacitor. The research indicates that the ammoniation/deamination mechanism is dominated by non-diffusion controlled pseudo capacitance behavior. 14 So far, the reported ammonium storage materials are basically MXene, 16 Prussian blue analogues, 17 conductive polymers (PANI) 18 and metal oxides (MoO 3 , V 2 O 5 , MnO x , Fe 5 -V 15 O 39 (OH) 9 $9H 2 O). 12,19,20 However, the performances achieved to date remain inferior to what lithium-ion batteries can do, showing limited capacity and cycling stability. Therefore, to achieve rechargeable AIBs with excellent performance, it is necessary to explore new electrodes for NH 4 + storage.
At the current stage, the discovery of these energy materials relies predominantly on experimental serendipity and the tryand-error experimental process that are inefficient and timeconsuming. Nevertheless, much evidence has shown that the discovery process of new energy materials could be signicantly accelerated by the data mining process and high throughput calculation. 21,22 Now, various experimental and computational repositories such as Inorganic Crystal Structure Database (ICSD), 23 Crystallography Open Database (COD), 24 the Materials Project, 25 and others store thousands of experimental and calculated structures, which already serve as potential batteries electrodes or still wait for such an opportunity.
Meanwhile, A. O. Boev et al. extracted 2800 initial structures from the material database and identied 33 potential compounds for cathode materials of lithium-oxygen batteries with low normalized surface energy. 26 Max Avdeev used highthroughput screening to conduct a detailed analysis of the 13 000 materials in ICSD, and identied the crystal structures featuring innite networks of pathways suitable for Li + , Na + , K + , Ag + , and Cu + ionic transport. 27 However, there is no report on the high-throughput screening method to determine the candidate electrode materials for ammonium-ion batteries.
As inspired by the ion exchange experiments, the compounds from ICSD (inorganic crystal structures database) 23 which contain K + ion were chosen. We replaced the K + ions in these compounds with NH 4 + to work as the input of our following screening process, since the K + and NH 4 + ions have the same valence and almost the same ionic radii (149 pm for K + and 148 pm for NH 4 + ). 28 34 (IV) 108 compounds were obtained by a lter of specic capacity greater than 100 mA h g −1 . (V) Aer the rst principle calculation, the 72 compounds were screened using the condition that the open circuit voltage (OCV) was higher than 3 V. (VI) The nal screening condition is that the volume expansion rate of the optimized structure is less than 10% compared with the Kcontained analog, and 27 compounds are selected (Fig. 1).

Bond valence energy landscape (BVEL) method
The bond-valence method 35 is the development of the principle of local charge neutrality (rst proposed by Pauling). The valence of an atom is the sum of the individual bond valences surrounding the atom. The results show that the dependence of S ij on the distance between the i th and j th ions R ij can be well described by exponential function.
where R 0 and b are empirical parameters. 36 As shown in S. Adams's work, 31 the bond valence site energy of i can then be interpreted as a result of a Morse-type interaction with the adjacent anions j, it can be combined with the Coulomb repulsion E repulsion of i with other immobile cations.
where r i and r j are the covalent radii of the respective cation (or anion) pair i, j and f is a screening factor (typically of the order f z 0.75). 37 It may be noted that for the purpose of analyzing E landscapes, Coulomb repulsions are considered only between mobile and immobile cations to reveal continuous pathways, while coulomb attraction terms are generally integrated into the Morse attraction term. The charge screening is based on an error function complement term E repulsion . The console utilities CrysFML (Crystallographic Fortran 95 Modules Library) which are developed by N. A. Katcho et al. 38 are used for bond-valence energy landscapes calculations. Small Python scripts have been written to bond the input and output between programs to reduce human intervention and facilitate Fig. 1 The schema diagram of the screening process. All data relating to screening process are included in the ESI. data management. Within the theoretical framework of bondvalence sum, the diffusion barriers (E a ) in three directions of a, b and c of the cell are obtained. The fundamental process that enables the functioning of most of today's rechargeable batteries is the reversible intercalation of ions into electrode. Ionic conductivity emerges as a paramount criterion. We abandon the structures with diffusion barrier higher than 0.3 eV.
2.2.2 Structure and specic capacity selection. Most of the cathode materials for Li-ion or Na-ion batteries have more than 3 elements in their chemical formulas. 39,40 For AIBs, we focus on compounds with the general formula of (NH 4 ) a M b (XY c ) d . And we also eliminate the compounds which have elements with low abundance and high price such as Sc, Y, In or rare-earth metals.
Specic capacity is an indicator to the amount of electric charge stored by the electroactive materials in a unit mass. The formula of the specic capacity is as follows: where n is the number of transferred electrons, M is the molar mass of the selected compounds, and F is Faraday constant (26 801 mA h mol −1 ). We selected compounds with theoretical specic capacity more than 100 mA h g −1 for the next round of screening. 108 kinds of materials were screened from 8221 types of materials.
2.2.3 Density functional theory (DFT) calculations. The density functional theory method has emerged as an integral and important part of the screening process for electrode materials design. All calculations were performed with the Vienna Ab initio Simulation Package (VASP), 41 within the projector augmented wave (PAW) approach. 42 The Python Materials Genomics (pymatgen) materials analysis library was used for all analyses. 43 All structural relaxations and total energy calculations were carried out using parameters similar to those used in the Materials Project. 44 The key parameters are the use of the Perdew-Burke-Ernzerhof (PBE) generalized-gradient approximation (GGA) 45 exchange correlation functional, an energy cutoff of 520 eV and a k-point mesh of at least 4377 per atom. The relaxation process is divided into two steps. First, keep the cell volume unchanged, optimize the atomic position, and then optimize the cell fully until the convergence criterion is reached. For structures with fractional occupancy in the database, VCA (virtual crystal approximation) 46 method is used. VCA method is to scale the local potential, the augmentation charges, and the non-local pseudopotential strength parameters of atoms occupied by fractions from the values provided. We also carried out the statications self-consistent and non-self-consistent calcul to explore the density of states and electronic band structure of compounds.
Open circle voltage (OCV) 47,48 is determined by the chemical potential difference between cathode and anode, and can be calculated as Table 1 27 potential electrode materials for ammonium-ion batteries after the screening. ID is the ICSD collection code of the compound containing K + before replacement, and E (eV) is the minimum potential barrier value calculated by BVEL. The dimension of the diffusion path (D) is judged by barrier energies along the three coordinate axes. Open circuit voltage OCV (V), B_g (eV) is the band gap. The c (mA h g −1 ) is the specific capacity. V (Å 3 ) is the unit cell volume of compounds containing K + , V ′ (Å 3 ) is the unit cell volume of compounds containing NH 4 + after replacement and optimization, and Ver (%) is the volume expansion rate where E cathode is dened as the free energy of the intercalated cathode. E anode is dened as the free energy of each atom of the anode (NH 4 + ). Z e represents the transferred charge. For NH 4 + , we choose a condensed phase similar to body centered cubic lattice, and Z is the valence number (Z = 1 for NH 4 + ). The widely used anode in AIBs is conductive polymer materials such as polyaniline (PANI) which has good electronic conductivity, high accommodation capabilities for large ions and light weight. 18 This anode has higher chemical potential compared with our "fake" pure NH 4 + lattice. Thus, our OCV values are overestimated can only work as upper limit of the expected OCV values.
To further evaluate the ionic conductivities, the nudged elastic band (NEB) 49,50 method based on DFT is adopted to identify ion migration paths and compute their corresponding energy barriers. Despite the success of the NEB method in characterizing the diffusion process in electrode, the signicant computational expense of NEB relative to standard DFT calculations, e.g., geometry relaxations and static energy calculations, has hampered its application to cover all the ltered compounds. Only the nal screening compounds are calculated to verify the diffusion barrier calculated by the BVEL method.

Screening overview
In the screening algorithm, only the rst screening method BVEL diffusion barrier calculation is empirical method. The rest of the ltering is based on rst principle calculations. The diffusion barrier, open circuit voltage, and specic capacity are designed for better battery performance. While the general formula of (NH 4 ) a M b (XY c ) d and smaller volume expansion rate compounds are selected to obtain more stable structures. Moreover, the smaller volume expansion rate means that the compound can be more likely synthesized by the ion exchange experiment.
From 8221 compounds containing K + in the ICSD database, we obtained 27 potential electrode materials for AIBs ( Table 1). The calculated OCV is in the range of 3.39 V to 6.85 V. The maximum OCV is obtained from NH 4 Zn(BeF 3 ) 3 which contains uorine atoms. The OCV of (NH 4 ) a M b (PO 4 ) d derivatives are about 5.0 V depending on the different metal ion involved. The specic capacity of selected compounds is in the range of 100.33 to 336.97 mA h g −1 . The maximum specic capacity is calculated from NH 4 Li 2 (BO 3 ) which contains only light elements. We also explored their electronic structures within the theoretical framework of density functional theory. Band structures of the screened compounds have been obtained, and the band gaps are shown in Table S6 in ESI. † Further, we have also performed DFT-based NEB calculations for 27 candidate compounds to analyze the feasibility of the screening algorithm and the diffusion properties of candidate materials (   (Fig. 2(b)) is a compound obtained by replacing K + from K 2 Ni(MoO 4 ) 2 ( Fig. 2(a)). The space group is P1, and NH 4 + can migrate along the a-axis and c-axis. Therefore, aer BVEL calculation, as shown in Fig. 2(c), the low-valued isosurface identies areas with a low energy barrier and therefore represents the most likely pathway for ion transport. In addition, Fig. 2(d) shows the charge density aer the DFT calculation. When we replace K + with NH 4 + , and aer structural relaxation, it is found that the unit cell has a small expansion ( Fig. 2(a) and (b)), the unit cell volume of K 2 Ni(MoO 4 ) 2 expanded from 1747.49 Å 3 to 1910.76 Å 3 (Tables  S4 and S5 in ESI †), At the same time, the symmetry of the structure also changed because of the difference between the tetrahedral structure of NH 4 + and the spherical structure of K + .
This expansion distortion will not cause the structure of the compound to collapse. From NEB calculation, it is revealed that the strong hydrogen bond makes the diffusion pattern of NH 4 + ions similar to the monkey swing ( Fig. 2(f)), which is consistent with the study of Ji's team. 11 And this diffusion mode is accompanied by the continuous formation and breaking of hydrogen bonds, which can show rapid electrode dynamics and further improve the electrochemical performance of AIBs. 3.1.2 Tunnel type. The tunnel electrode materials account for 25 of the 27 selected materials. To take a further look at NH 4 Fe(PO 4 )F, the minimum BVS mismatch path of NH 4 + shows obvious 3 dimension pathways. From the BVEL data map (isosurface = 0.58 e Bohr −3 ), ammonium-ion diffuses in a zig-zagshaped path (Fig. 3(c)), which is the same as reported in ref.
52 which the electrode material NaFeSO 4 F of Na-ion batteries was shown. 52 In these tunnel type electrodes, there is 1 dimension diffusing type electrode. The BVEL map of NH 4 -Zn(BeF 3 ) 3 shows a 1 dimension diffusion along the z-axis ( Fig. 3(g)), which is similar to the reported a-MoO 3 electrode. 53 It has a simple tunnel structure, and the formation and fracture of hydrogen bonds are still the primary way of its diffusion, which also guarantees ultrafast kinetics in the reversible insertion/ deinsertion process during cycling. 54 NH 4 CrPO 4 F, NH 4 (TiO) AsO 4 and (NH 4 ) 3 (BSb 4 O 13 ) also have very small diffusion barriers and large specic capacity, which is potential candidate for fast ammonium ion storage electrode.

Electronic structure
The preliminary idea to calculate the electronic band structure of a potential electrode material is to determine its metallic, semiconducting or insulating character. The structures and density of states diagrams are listed in Fig. S1-S27   . BVEL data (c), charge density diagram (d) and band structure calculated by DFT (e). The diffusion mode of ammonium ion is revealed by NEB calculation (f), in which ammonium is a colored atom, and the same color represents the same atom before and after diffusion.  55 Incorporating of metal ion can efficiently modulate the band gap of (NH 4 ) a M b (PO 4 ) d derivatives. The only exception is NH 4 (VO)(PO 4 ) which has much smaller band gap (1.55 eV). Also, there are ve (NH 4 ) a M b (Si c O d ) e derivatives. The band gap of these compound is in the range 0.04 eV to 5.03 eV. The maximum band gap is 6.14 eV calculated from uorid NH 4 Zn(BeF 3 ) 3 . The theoretical band gap of (NH 4 ) 2 (Zr 0.86 Ti 0.14 )(Si 3 (Table 2) show that there is small error between the NEB method based on DFT and the BVEL calculation results for most cases. The main cause of the deviation is that a "static" structure is used during the BVEL calculation. And the cell parameters of the compound remain unchanged aer NH 4 + substitution, which further leads to the difference between BVEL and the experimental (or DFT) barrier. For instance, the diffusion barrier of NH 4 Zn(BeF 3 ) 3 and NH 4 (SnO)(PO 4 ) using NEB based on DFT optimization shows ∼1 eV higher than the BVEL barrier, which is due to the signicant changes in structural parameters compared with its K precursor (specic data are shown in Tables S4 and S5 of ESI †). Despite deviations in the computed values, the high-throughput screening is capable to predict trends in structure-property relationships. The magnitude of deviations can differ substantially for different materials, environments, and thermodynamic factors. The results from the NEB method are more trustable and should have the quantitative agreement of dynamical properties with experimental results. Nevertheless, the BVEL method is still reliable as a rough selection of candidate battery electrode materials. Considering the complexity of the diffusion process of these compounds and the NEB paths considered may be unexhaustive, all the 27 compounds are reserved for further comprehensive study.

Summary
In this work, we have scanned 8221 K + -contained compounds from ICSD to nd the proper electrode material for ammoniumion batteries. The compounds with the exchange of K + ions with NH 4 + ions are used as the input of the following screening process. Aer the BVEL diffusion barrier lter, general formula lter, OCV screening, specic capacity screening, and volume expansion rate screening, we have successfully predicted 27 potential fast ammonium ion conductors for AIBs, all of which can stimulate further experimental studies and thorough theoretical investigations.
Our research is not exhaustive due to the rich structural chemistry of these ltered compounds, it gives an idea of the research interest in electrode materials for ammonium-ion batteries applications. Due to the simplicity of the BVEL method, its straightforward application to high-throughput schemes has some shortcomings. The empirical parameters of the BVEL method for NH 4 + ions are incomplete. This is the main factor that causes the miss. Although the ionic radii and valence of K + and NH 4 + ions are similar, the stability analysis aer the replacement would probably be insufficient, and additional phonon dispersion calculation would be required. Structures with partial occupations need to be properly treated, which requires more complex methodological architectures. Continued effort is undertaken to expand the databases used for screening and solving associated algorithmic and computational problems.

Data availability
All data generated or analyzed during this study are included in this article and its ESI. †

Conflicts of interest
The authors declare that they have no known competing nancial interests or personal relationships that could have appeared to inuence the work reported in this paper.